 
 
 
11.9.7  Row reduction to echelon form in ℤ/pℤ
In Xcas mode, Rref is simply the inert form of
rref; namely, it returns rref without
evaluating it (see Section 15.7.3).
In Maple mode, the Rref command
can additionally be used in conjunction with mod to
find the reduced row echelon form of a matrix whose elements are in
ℤ/pℤ.
- 
In Maple mode, Rref takes
A, a matrix with elements in ℤ/pℤ.
- Rref(A) returns the reduced row echelon form of A.
Example
Solve in ℤ/13ℤ:
Input in Xcas mode:
| Rref([[1,2,9] mod 13,[3,10,0] mod 13]) | 
To actually get the reduced echelon form, enter:
|  | | |  | | ⎡ ⎢
 ⎣
 | | 1%13 | 0%13 | 3%13 |  | 0%13 | 1%13 | 3%13 | 
 | ⎤ ⎥
 ⎦
 | 
 | 
 |  |  |  |  |  |  |  |  |  |  | 
 | 
Input in Maple mode:
| Rref([[1,2,9],[3,10,0]] mod 13) | 
In both cases you conclude that x=3%13 and y=3%13.
 
 
